Answer:
pH = 9.58
Explanation:
First of all, we need to determine the molarity of the solution.
We determine the molar mass of morphine:
12g/m . 17 + 1 g/m . 19 + 14 g/m + 16 g/m . 3 = 285.34 g/m
molar mass g/m, is the same as mg/mm
25 mg . 1 mmol / 285.34 mg = 0.0876 mmoles / 100 mL = 8.76×10⁻⁴ M
In diltuted solution, we must consider water.
Mass balance for morphine = [Morphine] + [Protonated Morphine]
8.76×10⁻⁴ M = [Morphine] + [Protonated Morphine]
As Kb is too small, I can skipped, the [Protonated Morphine]
8.76×10⁻⁴ M = [Morphine]
In the charge balance I will have:
[OH⁻] = [H⁺ morphine] + [H⁺]
Let's go to the Kb expression
Morphine + H₂O ⇄ MorphineH⁺ + OH⁻ Kb
Kb = [MorphineH⁺] [OH⁻] / [Morphine]
Kb = [MorphineH⁺] [OH⁻] / 8.76×10⁻⁴ M
So now, we need to clear [MorphineH⁺] to replace it in the charge balance
Kb . 8.76×10⁻⁴ M / [OH⁻] = [MorphineH⁺]
Now, the only unknown value is the [OH⁻]
[OH⁻] = Kb . 8.76×10⁻⁴ M / [OH⁻] + Kw/[OH⁻]
Remember that Kw = [H⁺] . [OH⁻]
[H⁺] = Kw/[OH⁻]
[OH⁻]² = 1.62×10⁻⁶ . 8.76×10⁻⁴ + 1×10⁻¹⁴
[OH⁻] = √(1.62×10⁻⁶ . 8.76×10⁻⁴ + 1×10⁻¹⁴)
[OH⁻] = 3.76×10⁻⁵ → - log [OH⁻] = pOH = 4.42
pH = 14 - pOH → 14 - 4.42 = 9.58
